Interactive Tools

Research Demonstrations

These interactive tools demonstrate concepts from my research in conformal prediction, uncertainty quantification, and statistical machine learning.

Kumaraswamy Mixture Model: Conformal Prediction Explorer

An interactive visualization demonstrating conformal prediction with Kumaraswamy mixture models on $[0,1]$. This tool shows how label-conditional conformal calibration partitions the feature space and induces region-specific posteriors.

Key Concepts Illustrated:

• Analytical tractability of Kumaraswamy distributions (closed-form CDF)
• Conformal cutpoint computation: $L = (1-(1-\alpha_1)^{1/b_1})^{1/a_1}$, $U = (1-\alpha_0^{1/b_0})^{1/a_0}$
• Region-specific marginals and posterior distributions
• Information-theoretic metrics (binary entropy) for prediction sets
• The distinction between coverage guarantees (validity) and prediction quality (optimality)

Interactive Controls:

• Shape parameters ($a_0, b_0, a_1, b_1$) for class-conditional distributions
• Prior probability $c = P(Y=0)$
• Miscoverage levels $\alpha_0, \alpha_1$
• Five preset configurations demonstrating different scenarios

Launch Tool

Related Publication:
Zwart, P.H. (2025). “Probabilistic Conformal Coverage Guarantees in Small-Data Settings.” arXiv:2509.15349

Technical Details

All calculations use closed-form expressions—no numerical integration required. The Kumaraswamy distribution’s analytical CDF enables exact computation of:

• Region masses: $m([a,b]) = c[F_0(b)-F_0(a)] + (1-c)[F_1(b)-F_1(a)]$
• In-region rates: $\bar{p}([a,b]) = (1-c)[F_1(b)-F_1(a)] / m([a,b])$
• Binary entropy: $H(p) = -p \log_2(p) - (1-p) \log_2(1-p)$

Three regions are determined by $r_- = \min(L,U)$ and $r_+ = \max(L,U)$:

• If $L < U$: Regions $R_0 = [0, r_-)$, $R_M = [r_-, r_+)$ (hedge), $R_1 = [r_+, 1]$
• If $L > U$: Regions $R_0 = [0, r_-)$, $R_M = [r_-, r_+)$ (abstain), $R_1 = [r_+, 1]$

Upcoming Tools

Additional interactive demonstrations are in development:

Quantile Regression for Autonomous Experimentation
Visualizing adaptive data acquisition strategies using conformalized quantile regression

Small Sample Beta Correction (SSBC) Demo
Interactive exploration of PAC coverage guarantees in small-sample settings

Representation Learning Visualizations
Tools for exploring emergent representations in conformal quantile regression

Source Code

The source code for these tools is available on GitHub and can be adapted for your own research or educational purposes.

These tools complement my research on conformal prediction and uncertainty quantification. For theoretical background, see my Publications page.